$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x + 2$ and $ JT = 8x + 10$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x + 2} = {8x + 10}$ Solve for $x$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({8}) + 2$ $ JT = 8({8}) + 10$ $ CJ = 72 + 2$ $ JT = 64 + 10$ $ CJ = 74$ $ JT = 74$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {74} + {74}$ $ CT = 148$